Electronic States, Spin-Orbit Coupling and Magnetism in Germanium 60° Dislocations

Defects in semiconductors have recently attracted renewed interest owing to their potential in novel quantum applications. Here we investigate the electronic and magnetic properties induced by 60° dislocations in Ge. Using large-scale DFT calculations, we determine the band structure for both the shuffle and glide sets in their lowest-energy configurations. We also perform charged-defect calculations to aid in the interpretation of complex photoluminescence spectra observed in epitaxial Ge layers. The band structure for the shuffle set reveals defect-induced dispersive bands localized within the band gap near the Γ point, whereas for the glide set, we observe strong overlap with the conduction band. Defect-induced band splitting evident away from Γ reveals Rashba-Dresselhaus spin-orbit coupling, an effect previously reported only for screw dislocations. Remarkably, we find evidence that specific dislocation arrangements can stabilize antiferromagnetic ordering with sizable local magnetic moments and considerable exchange splitting between opposite spin states. These results uncover rich physics in Ge dislocations through the combination of spin-orbit coupling and magnetic ordering, potentially enabling novel defect-based functionalities in Ge devices.

💡 Research Summary

This paper presents a comprehensive first‑principles investigation of 60° dislocations in germanium, focusing on their structural stability, electronic band structure, spin‑orbit coupling (SOC), and magnetic ordering. Using large supercells (up to 768 atoms) and the meta‑GGA mBJ functional together with explicit SOC, the authors model both the shuffle (S3 reconstruction) and glide core configurations. Energetically, the glide core is the most stable, lying 1.22 eV Å⁻¹ below the shuffle S3 core, while among shuffle candidates S3 is the lowest‑energy reconstruction (S1 → S2 → S3).

Electronic structure calculations reveal that the shuffle S3 core introduces two highly localized, dispersive defect bands deep within the band gap. These bands are degenerate at the Γ point but split up to ~20 meV away from Γ, displaying opposite spin polarization. A detailed spin‑texture analysis shows a helical pattern characteristic of Rashba‑Dresselhaus SOC, indicating that the screw component of the mixed edge‑screw 60° dislocation dominates the SOC physics, similar to previously reported pure screw dislocations.

In contrast, the glide core also hosts defect‑derived bands, but they lie close to or overlap with the conduction band minimum, resulting in a much weaker SOC signature (maximum splitting ~7 meV) and a less discernible spin texture.

To connect theory with experiment, the authors employ a transition‑charge model, calculating formation energies of the dislocation cores in multiple charge states as a function of the Fermi level. This yields thermodynamic transition levels that can be directly compared with photoluminescence (PL) measurements of epitaxial Ge layers, providing a practical tool for defect identification.

Perhaps the most striking finding is the emergence of antiferromagnetic (AFM) ordering in the shuffle S3 configuration. The localized defect states generate a sharp density‑of‑states peak ~0.13 eV above the valence‑band maximum, leading to partial occupation and a local magnetic moment of roughly 0.5 μB per core atom. Spin‑polarized calculations show an exchange splitting of ~0.15 eV between opposite spin channels, stabilizing an AFM arrangement of neighboring cores. This demonstrates that 60° dislocations can simultaneously act as electronic traps, SOC sources, and magnetic centers.

The study also compares two dipole supercell arrangements: identical‑type dipoles (shuffle‑shuffle or glide‑glide) and mixed shuffle‑glide dipoles. Identical dipoles emphasize strong core‑core coupling, useful for exploring collective magnetic effects, while mixed dipoles reduce artificial band folding and better represent isolated dislocations.

Overall, the work establishes that germanium 60° dislocations are rich platforms where electronic, spin, and magnetic degrees of freedom intertwine. The identified deep‑gap defect bands, Rashba‑Dresselhaus SOC, and AFM ordering suggest new avenues for defect‑engineered functionalities in Ge‑based electronic, optoelectronic, and spintronic devices, such as spin filters, quantum bits, or charge‑sensing elements.